kstest:计算Kolmogorov-Smirnov拟合优度检验

Kolmogorov-Smirnov Goodness-of-Fit Test === [![NPM version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][codecov-image]][codecov-url] [![Dependencies][dependencies-image]][dependencies-url] > One-sample Kolmogorov-Smirnov goodness-of-fit test. ## Installation ``` bash $ npm install compute-kstest ``` For use in the browser, use [browserify](https://github.com/substack/node-browserify). ## Usage ``` var kstest = require( 'compute-kstest' ); ``` ### kstest( x, y[, opts] ) For a numeric [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array) or [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays) `x`, a Kolmogorov-Smirnov goodness-of-fit is computed for the null hypothesis that the values of `x` come from the distribution specified by `y`. `y` can be either a [`string`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/String) with the name of the distribution to test against, or a [`function`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Function). In the latter case, `y` is expected to be the cumulative distribution function (CDF) of the distribution to test against. The function returns an object holding the calculated test statistic `T` and the `pValue` of the test. ```javascript var randUnif = require( 'distributions-uniform-random' ), x, out; // Set seed randUnif.seed = 54 x = randUnif( 100 ); out = kstest( x, 'uniform' ) // { pValue: ~0.872, T: ~0.058 } ``` The returned object comes with a `.toString()` method which when invoked will print a formatted output of the results of the hypothesis test. ```javascript x = randUnif( 100 ) out = kstest( x, 'normal' ); console.log( out.toString() ); /* Kolmogorov-Smirnov goodness-of-fit test. null hypothesis: the CDF of `x` is equal equal to the reference CDF. test statistic: 0.5019 p-value: 0 */ ``` By default, the parameters of the distribution specified by `y` are set to their standard values (see the documentation for the respective [distribution](https://github.com/distributions-io)). To specify custom parameters, set the corresponding options: ```javascript x = randUnif( 100, { 'a': 10, 'b': 20 }) // Test against U(0,1) out = kstest( x, 'uniform' ); // returns { pValue: 0, T: 1 } // Test against U(10,20) out = kstest( x, 'uniform', { 'a': 10, 'b': 20 }); // returns { pValue: ~0.826, T: ~0.061 } ``` In addition to the respective distribution parameters, the function accepts the following `options`: * __alternative__: Either `two-sided`, `less` or `greater`. Indicates whether the alternative hyptothesis is that the true distribution of `x` is not equal to the reference distribution specified by `y` (`two-sided`), whether it is `less` than the reference distribution or `greater` than the reference distribution. Default: `two-sided`. * __sorted__: `boolean` indicating if the `x` [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array) is in sorted order (ascending). Default: `false`. By default, the function tests the null hyptothesis that the true distribution of `x` and the reference distribution `y` are equal to each other against the alternative that they are not equal. To carry out a one-sided hyptothesis test, set the `alternative` option to either `less` or `greater`. ```javascript x = randUnif( 100 ) out = kstest( x, 'uniform', { 'alternative': 'less' }); // returns { pValue: ~0.647, T: ~0.045 } out = kstest( x, 'uniform', { 'alternative': 'greater' }); // returns { pValue: ~0.179, T: ~0.091 } ``` To perform the Kolmogorov-Smirnov test, the data has to be sorted in ascending order. If the data in `x` are already sorted, set the `sorted` option to `true` to speed up the computation. ```javascript x = [ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 ] out = kstest( x, 'uniform', { 'sorted': true }); // returns { pValue: ~1, T: 0.1 } ``` ## Examples ``` javascript var kstest = require( 'compute-kstest' ), x, out, table; // Values drawn from a Normal(3,1) distribution x = [ 1.956335, 4.188998, 2.000942, 2.908463, 3.673476, 4.395047, 3.367432, 2.074397, 1.754223, 3.943273, 1.907448, 2.239214, 3.205089, 1.650116, 3.772828, 2.969861, 2.453575, 2.371188, 4.207656, 2.716989 ]; // Test against N(0,1) out = kstest( x, 'normal' ); // returns { pValue: 0, T: ~0.951 } table = out.toString(); /* Kolmogorov-Smirnov goodness-of-fit test. null hypothesis: the CDF of `x` is equal equal to the reference CDF. test statistic: 0.9505 p-value: 0 */ // Test against N(3,1) out = kstest( x, 'normal', { 'mu': 3 }); // returns { pValue: ~0.647, T: ~0.157 } table = out.toString(); /* Kolmogorov-Smirnov goodness-of-fit test. null hypothesis: the CDF of `x` is equal equal to the reference CDF. test statistic: 0.1576 p-value: 0.6467 */ ``` To run the example code from the top-level application directory, ``` bash $ node ./examples/index.js ``` ## Tests ### Unit Unit tests use the [Mocha](http://mochajs.org/) test framework with [Chai](http://chaijs.com) assertions. To run the tests, execute the following command in the top-level application directory: ``` bash $ make test ``` All new feature development should have corresponding unit tests to validate correct functionality. ### Test Coverage This repository uses [Istanbul](https://github.com/gotwarlost/istanbul) as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory: ``` bash $ make test-cov ``` Istanbul creates a `./reports/coverage` directory. To access an HTML version of the report, ``` bash $ make view-cov ``` --- ## License [MIT license](http://opensource.org/licenses/MIT). ## Copyright Copyright © 2015. The [Compute.io](https://github.com/compute-io) Authors. 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